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\begin{eqnarray}
\mathcal{L} &=& \sum_i (p_i * \pi)^2 + \lambda (\pi \cdot \infty) \\
\frac{\delta \mathcal{L}}{\delta \pi} & = & 2\sum_i p_i(p_i \cdot \pi) - \lambda \infty = 0 \\
\Rightarrow -2 \sum_i p_i(p_i \cdot \pi) \cdot \vec{o} & = & \lambda \\
\Rightarrow \frac{\delta \mathcal{L}}{\delta \pi} = 2 \sum_i p_i(p_i \cdot \pi) + (2 \sum_i p_i(p_i \cdot \pi) \cdot \vec{o}) \infty & = & 0 \\
\Rightarrow \sum_i p_i(p_i \cdot \pi) + \infty p_i(p_i \cdot \pi) \cdot \vec{o} & = & 0 \\
\Rightarrow \sum_i p_i p_i^T M \pi + \infty p_i^T M \vec{o} p_i^T M \pi & = & 0 \\
\Rightarrow \sum_i (p_i p_i^T M + \infty p_i ^T M \vec{o} p_i^T M) \pi & = & 0
\end{eqnarray}
Nu kunnen we oplossen door de kern te nemen van A:
\[ A = \sum_i p_i p_i^T M + \infty p_i^T M \vec{o} p_i^T M \]

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